Small- and medium-sized enterprises (SMEs) establish asymmetric research and development (R&D) alliance with core enterprises to improve innovation efficiency. Unfortunately, the gap in the status and bargaining power between enterprises in such partnerships makes the intellectual property risk situation complicated. While gaining support and assistance from core enterprises, SMEs face the risk of exposing their core knowledge and key resources, which seriously affects the stability of R&D alliance and the sustainability of cooperative innovation. How to protect the intellectual property rights of SMEs in the asymmetric R&D alliance and improve the alliance’s stability is an urgent problem to be solved. Based on the theory of resource dependence and transaction cost, this study uses 260 high-tech companies participating in the asymmetric R&D alliance as a sample to conduct empirical research from the perspective of SMEs in a weak position. The purpose of this study is to sort out the types of intellectual property risks in the alliance and clarify the relationship between them and the stability of asymmetric R&D alliance. Furthermore, this study examines the moderating effects of contract governance mechanisms and relational contracts to explore effective governance mechanisms at the alliance level. Empirical results show that the intellectual property investment risk and the intellectual property loss risk have a significant negative impact on the stability of asymmetric R&D alliance. The contract governance mechanism negatively moderates the impact of intellectual property investment risk on the stability of the asymmetric R&D alliance. The relationship governance mechanism negatively moderates the impact of intellectual property loss risk on the stability of the asymmetric R&D alliance. The contract and relationship governance mechanism jointly negatively moderate the impact of intellectual property investment risk and loss risk on the stability of the asymmetric R&D alliance.